G. VaradhanUniversity
of North Carolina, S. KrishnanAT&T Research Labs,
T. V. N. Sriram, and D. ManochaUniversity of North Carolina

We present an algorithm for
complete path planning for translating polyhedral robots in three dimensions.We
compute a roadmap of the free space that captures its connectivity. The
roadmap is constructed without computing an explicit representation of the
free space. It encodes the complete connectivity of free space and allows
us to perform exact path planning. We construct a roadmap by performing
a sampling of the free space in a deterministic fashion.We obtain a set
of deterministic samples by generating an adaptive volumetric grid. Our
algorithm is simple to implement and uses two tests: a complex cell test
and a star-shaped test during sample generation. These tests can be efficiently
performed on polyhedral objects using max-norm distance computation and
linear programming. We demonstrate the performance of our algorithm on environments
with very small narrow passages or no collision-free paths.